Misc 12,
Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = ∅.
A ∩ B should be non-empty,
i.e. there should be some common element between A & B
Similarly,
B ∩ C should be non-empty,
i.e. there should be some common element between B & C
A ∩ C should be non-empty,
i.e. there should be some common element between A & C
Also, given that A ∩ B ∩ C is a null set,
i.e. there should be not be any element common between A, B & C
Let A = {0, 1},
B = {1, 2},
and C = {2, 0}.
Now,
A ∩ B = {1},
B ∩ C = {2},
and A ∩ C = {0}.
∴ A ∩ B, B ∩ C, and A ∩ C are non-empty.
However, A ∩ B ∩ C = ∅